Lab 10: Iterators and Generators
Due at 11:59:59 pm on 11/14/2023.

Starter Files

Download lab10.zip. Inside the archive, you will find starter files for the questions in this lab, along with a copy of the OK autograder.

Iterables and Iterators

Remember the for loop? (We really hope so.) The object the for loop iterates over must be an iterable! An iterable is a way of representing explicit sequences (like lists or strings) as well as implicit sequences (like the natural numbers 1, 2, 3, ...).

for elem in iterable:
    # do something

for loops only work with iterables. This means the object you want to use a for loop on must implement the iterable interface. To implement the iterable interface, an object must define an __iter__ method that returns an object that implements the iterator interface.
To also implement the iterator interface, an object must define a __next__ method to compute and return the next element in the sequence. If the iterator exhausts the sequence, it raises StopIteration to send a signal to indicate that it reaches the end.

An iterable object can create an arbitrary amount of iterator objects. In addition, the iterators are independent of each other; in other words they can have a different position in the sequence.

Here is a table summarizing the required methods of the iterable and iterator interfaces/protocols. Python also has more documentation about iterator types.

In Python, an iterator must also be an iterable. In other words, it must have a __iter__ method that returns itself (with the current state unaltered).

Analogy: an iterable is like a book (one can flip through the pages) and an iterator is a bookmark (saves the position and can locate the next page). Calling __iter__ on a book gives you a new bookmark independent of other bookmarks, but calling __iter__ on a bookmark gives you the bookmark itself, without changing its position at all.

Here is an example of a class definition for an object that implements the iterator interface:

class AnIterator:
    def __init__(self):
        self.current = 0

    def __next__(self):
        if self.current > 5:
            raise StopIteration
        self.current += 1
        return self.current

    def __iter__(self):
        return self

Let's go ahead and try out our new toy.

>>> for num in AnIterator():
...     print(num)
1
2
3
4
5
6

This is somewhat equivalent to running:

t = AnIterator()
t = iter(t) # iter(t) is the same as t.__iter__()
try:
    while True:
        # next(t) is the same as t.__next__()
        print(next(t))
except StopIteration as e:
    pass

Question 1: Does it work?

Consider the following iterators. Which ones work and which ones don't? Why?

Use OK to test your knowledge with the following conceptual questions:

python3 ok -q does_it_work -u

class IteratorA:
    def __init__(self):
        self.start = 10

    def __next__(self):
        if self.start > 100:
            raise StopIteration
        self.start += 20
        return self.start

    def __iter__(self):
        return self

No problem, this is a beautiful iterator.

class IteratorB:
    def __init__(self):
        self.start = 5

    def __iter__(self):
        return self

Oh no! Where is __next__? This fails to implement the iterator interface because calling __iter__ doesn't return something that has a __next__ method.

class IteratorC:
    def __init__(self):
        self.start = 5

    def __next__(self):
        if self.start == 10:
            raise StopIteration
        self.start += 1
        return self.start

This also fails to implement the iterator interface. Without the __iter__ method, the for loop will error. The for loop needs to call __iter__ first because some objects might not implement the __next__ method themselves, but calling __iter__ will return an object that does.

class IteratorD:
    def __init__(self):
        self.start = 1

    def __next__(self):
        self.start += 1
        return self.start

    def __iter__(self):
        return self

This is technically an iterator, because it implements both __iter__ and __next__. Notice that it's an infinite sequence! Sequences like these are the reason iterators are useful. Because iterators delay computation, we can use a finite amount of memory to represent an infinitely long sequence.

Question 2: Str

Write an iterator that takes a string as input and outputs the letters in order when iterated over.

class Str:
    def __init__(self, str):
        self.str = str
    def __iter__(self):
        return iter(self.str)

class Str:
    "*** YOUR CODE HERE ***"
    def __init__(self, str):
        self.str = str
        self.i = -1

    def __iter__(self):
        return self

    def __next__(self):
        self.i += 1
        if self.i >= len(self.str):
            raise StopIteration
        return self.str[self.i]

There is no doctest for this problem. Test this on your own! We recommend starting with an interactive python shell python3 -i lab10.py. Here is an example sequence of commands:

>>> hey_iter = Str('hey')
>>> next(hey_iter)
'h'
>>> next(hey_iter)
'e'
>>> next(hey_iter)
'y'
>>> next(hey_iter)
StopIteration

Generators

A generator function returns a special type of iterator called a generator object. Such functions can be written using a yield statement:

def <generator_fn_name>():
    <somevariable> = <something>
    while <predicate>:
        yield <something>
        <increment somevariable>

Calling a generator function (a function with a yield statement in it) makes it return a generator object rather than executing the body of the function.

The reason we say a generator object is a special type of iterator is that it has all the properties of an iterator, meaning that:

• Calling the __iter__ method makes a generator object return itself without modifying its current state.
• Calling the __next__ method makes a generator object compute and return the next object in its sequence. If the sequence is exhausted, StopIteration is raised.
• Typically, a generator should not restart unless it's defined that way. But calling the generator function returns a brand new generator object (like calling __iter__ on an iterable object).

However, they do have some fundamental differences:

• An iterator is a class with __next__ and __iter__ explicitly defined, but a generator can be written as a mere function with a yield in it.
• __iter__ in an iterator uses return, but a generator uses yield.

• A generator "remembers" its state for the next __next__ call. Therefore, the first __next__ call works like this:

  1. Enter the function, run until the line with yield.
  2. Return the value in the yield statement, but remember the state of the function for future __next__ calls.

  And subsequent __next__ calls work like this:

  1. Re-enter the function, start at the line after yield, and run until the next yield statement.
  2. Return the value in the yield statement, but remember the state of the function for future __next__ calls.

Use OK to test your knowledge with the following What would Python print questions:

python3 ok -q generators -u

def generator():
    print("Starting here")
    i = 0
    while i < 6:
        print("Before yield")
        yield i
        print("After yield")
        i += 1

>>> g = generator()
>>> g # what type of object is this?
______
<generator object ...>
>>> g == iter(g) # equivalent of g.__iter__()
______
True
>>> next(g) # equivalent of g.__next__()
______
Starting here
Before yield
0
>>> next(g)
______
After yield
Before yield
1
>>> next(g)
______
After yield
Before yield
2

Trace through the code and make sure you know where and why each statement is printed.

You might have noticed from the Iterators section that IteratorB, which didn't define a __next__ method, failed to run in the for loop. However, this is not always the case.

class IterGen:
    def __init__(self):
        self.start = 5

    def __iter__(self):
        while self.start < 10:
            self.start += 1
            yield self.start

for i in IterGen():
    print(i)

Why does this iterable work without defining a __next__ method?

The for loop only expects the object returned by __iter__ to have a __next__ method. The __iter__ method is a generator function because of the yield statement in the body. Therefore, when __iter__ is called, it returns a generator object, which you can call __next__ on.

Question 3: Countdown

Write a generator that counts down to 0.

Write it in both ways: using a generator function on its own, and within the __iter__ method of a class.

def countdown(n):
    """
    >>> from types import GeneratorType
    >>> type(countdown(0)) is GeneratorType # countdown is a generator
    True
    >>> for number in countdown(5):
    ...     print(number)
    ...
    5
    4
    3
    2
    1
    0
    """
    "*** YOUR CODE HERE ***"
    while n >= 0:
        yield n
        n = n - 1

Use OK to test your code:

python3 ok -q countdown

class Countdown:
    """
    >>> from types import GeneratorType
    >>> type(Countdown(0)) is GeneratorType # Countdown is an iterator
    False
    >>> for number in Countdown(5):
    ...     print(number)
    ...
    5
    4
    3
    2
    1
    0
    """
    "*** YOUR CODE HERE ***"
    def __init__(self, cur):
        self.cur = cur

    def __iter__(self):
        return self

    def __next__(self):
        result = self.cur
        if result < 0:
            raise StopIteration
        self.cur -= 1
        return result

# Alternate solution that makes __iter__ a generator function:
class Countdown:
    def __init__(self, cur):
        self.cur = cur

    def __iter__(self):
        while self.cur >= 0:
            yield self.cur
            self.cur -= 1

Hint: Is it possible to not have a __next__ method in Countdown?

Use OK to test your code:

python3 ok -q Countdown

Question 4: Primes

Write a generator that generates prime numbers. Fill out the is_prime helper function and use that to create your generator.

def is_prime(n):
    """
    Return True if n is prime, false otherwise.

    >>> is_prime(1)
    False
    >>> is_prime(2)
    True
    >>> is_prime(19)
    True
    """
    "*** YOUR CODE HERE ***"
    if n < 2:
        return False
    counter = 2
    while counter <= sqrt(n):
        if n % counter == 0:
            return False
        counter += 1
    return True

def primes():
    """
    An infinite generator that outputs primes. 

    >>> p = primes()
    >>> for i in range(3):
    ...     print(next(p))
    ...
    2
    3
    5
    """
    "*** YOUR CODE HERE ***"
    num = 0
    while True:
        if is_prime(num):
            yield num
        num += 1

Use OK to test your code:

python3 ok -q is_prime

Use OK to test your code:

python3 ok -q primes

Question 5: Generate permutations

Given a list of unique elements, a permutation of the list is a reordering of the elements. For example, [2, 1, 3], [1, 3, 2], and [3, 2, 1] are all permutations of the list [1, 2, 3].

Implement generate_perms, a generator function which takes in a lst and yields all the unique permutations of lst one at a time (see doctest for examples).

def generate_perms(lst):
    """
    Generates the permutations of lst one by one.
    >>> perms = generate_perms([1, 2, 3])
    >>> hasattr(perms, '__next__')
    True
    >>> p = list(perms)
    >>> p.sort()
    >>> p
    [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]
    """
    if lst == []:
        "*** YOUR CODE HERE ***"
        yield []
    else:
        for perm in generate_perms(lst[1:]):
            for i in range(len(lst)):
                "*** YOUR CODE HERE ***"
                yield perm[:i] + [lst[0]] + perm[i:]

Use OK to test your code:

python3 ok -q generate_perms

Feel free to replace the for loops with list comprehensions if you would rather use that.

Submission

When you are done, submit your file to Gradescope. You only need to upload the following files:

• lab10.py